Causal State Estimation and the Heisenberg Uncertainty Principle
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arXiv
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| Autori principali: | , , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910563974512640 |
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| author | Chen, Junxin Lane, Benjamin B. Direkci, Su Ganapathy, Dhruva Yin, Xinghui Mavalvala, Nergis Chen, Yanbei Sudhir, Vivishek |
| author_facet | Chen, Junxin Lane, Benjamin B. Direkci, Su Ganapathy, Dhruva Yin, Xinghui Mavalvala, Nergis Chen, Yanbei Sudhir, Vivishek |
| contents | The observables of a noisy quantum system can be estimated by appropriately filtering the records of their continuous measurement. Such filtering is relevant for state estimation and measurement-based quantum feedback control. It is therefore imperative that the observables estimated through a causal filter satisfy the Heisenberg uncertainty principle. In the Markovian setting, prior work implicitly guarantees this requirement. We show that any causal estimate of linear observables of a linear, but not necessarily Markovian, system will satisfy the uncertainty principle. In particular, this is true irrespective of any feedback control of the system and of where in the feedback loop -- inside or outside -- the measurement record is accessed. Indeed, causal estimators using the in-loop measurement record can be as precise as those using the out-of-loop record. These results clarify the role of causal estimators to a large class of quantum systems, restores the equanimity of in-loop and out-of-loop measurements in their estimation and control, and simplifies future experiments on measurement-based quantum feedback control. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14476 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Causal State Estimation and the Heisenberg Uncertainty Principle Chen, Junxin Lane, Benjamin B. Direkci, Su Ganapathy, Dhruva Yin, Xinghui Mavalvala, Nergis Chen, Yanbei Sudhir, Vivishek Quantum Physics The observables of a noisy quantum system can be estimated by appropriately filtering the records of their continuous measurement. Such filtering is relevant for state estimation and measurement-based quantum feedback control. It is therefore imperative that the observables estimated through a causal filter satisfy the Heisenberg uncertainty principle. In the Markovian setting, prior work implicitly guarantees this requirement. We show that any causal estimate of linear observables of a linear, but not necessarily Markovian, system will satisfy the uncertainty principle. In particular, this is true irrespective of any feedback control of the system and of where in the feedback loop -- inside or outside -- the measurement record is accessed. Indeed, causal estimators using the in-loop measurement record can be as precise as those using the out-of-loop record. These results clarify the role of causal estimators to a large class of quantum systems, restores the equanimity of in-loop and out-of-loop measurements in their estimation and control, and simplifies future experiments on measurement-based quantum feedback control. |
| title | Causal State Estimation and the Heisenberg Uncertainty Principle |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2304.14476 |